Opinion Formation and Phase Transitions in a Probabilistic Cellular Automaton with Two Absorbing States

Abstract

Abstract. We discuss the process of opinion formation in a completely homogeneous, democratic population using a class of probabilistic cellular automata models with two absorbing states. Each individual can have one of two opinions that can change according to that of his neighbors. It is dominated by an overwhelming majority and can disagree against a marginal one. We present the phase diagram in the mean field approximation and from numerical experiments for the simplest nontrivial case. For arbitrarily large neighborhoods we discuss the mean field results for a non-conformist society, where each individual adheres to the overwhelming majority of its neighbors and choses an opposite opinion in other cases. Mean field results and preliminary lattice simulations with long-range connections among individuals show the presence of coherent temporal oscillations of the population. Modeling social pressure and political transitionsWhat happens to a society when a large fraction of people switches from a conformist to a non-conformist attitude? Is the transition smooth or revolutionary? These important questions, whose answers can make the difference between two well-known political points of view, is approached using a theoretical model, in the spirit of Latané's social impact theory [1,2].We assume that one's own inclination towards political choices originates from a mixture of a certain degree of conformism and non-conformism. Conformists tend to agree with the local community majority, that is with the average opinion in a given neighborhood, while non-conformists do the opposite. However, an overwhelming majority in the neighborhood (which includes the subject itself) is always followed.We shall study here the case of a homogeneous population, i.e. a homogeneous democratic society. 1 It may be considered as the annealed version of a 1 The case with strong leader was studied in Ref [3].

Evolutionary Daisyworld models: A new approach to studying complex adaptive systems

“…Public opinion is another example of complex adaptive systems (CAS), where an emergent behavior (public opinion) appears as a consequence of individual or local interactions (Miller and Page, 2007;Van Ginneken, 2003). In models of collective opinions based on cellular automata individuals interact with their neighbors (Alves et al, 2002;Bagnoli et al" 2002;Tipan Verella and Wardak, 2008). Under this approach, individuals are modelled as cells, the interaction between people is governed by micro-rules, and the spread of opinions is seen as a diffusive process.…”

“…Therefore, both the global opinion (7) and the individual preferences (7) influence each other. Contrary to most of the models about evolution of opinion (Alves et al, 2002;Bagnoli et al, 2002;Tipan Verella and Wardak, 2008) our model does not explicitly consider local interactions (indeed, at present, contact with our neighbors is highly restricted). Instead, agents interaction is mediated by a public opinion that is broadcasted through mass media, mainly TV, newspapers and radio.…”

“…The interaction between agents and the environment is also fundamental in sociology. The model defined in this paper is applied to study the formation and evolution of social opinions (Alves et al, 2002;Bagnoli et al, 2002;Tipan Verella and Wardak, 2008;Van Ginneken, 2003). In this sense, this ecologically inspired evolutionary algorithm can be viewed as a problem solving tool available to other disciplines.…”

Conservative Reversible Elementary Cellular Automata and their Quantum Computations

“…These two different possibilities are termed as uniform and hybrid CA, respectively [12,32,58,92]. While the next state function (rule) in general is deterministic, there are variations in which the rule sets are probabilistic [8,10,27] or fuzzy [24]. CA rules can be time-independent rules or time-dependent rules in which alternate rules at different time steps are used.…”

Chaos in a Simple Cellular Automaton Model of a Uniform Society

“…Technically, it is an extension of a probabilistic cellular automata with a very rich phase diagram [5], whose mean-field approximation was described in Ref. [6]. A detailed investigation of its behavior will be illustrated elsewhere [7].…”